Question

use the expression below to complete the following tasks.
$(3a^2 - 5ab + b^2) - (-3a^2 + 2b^2 + 8ab)$
what is the additive inverse of the polynomial being subtracted?

• $-3a^2 - 2b^2 - 8ab$
• $-3a^2 + 2b^2 - 8ab$
• $3a^2 - 2b^2 - 8ab$
• $3a^2 + 2b^2 + 8ab$

complete
after you rewrite subtraction as addition of the additive inverse, how can the like terms be grouped?

• $3a^2 + (-3a^2) + (-5ab + 8ab) + b^2 + (-2b^2)$
• $3a^2 + (-3a^2) + (-5ab + 8ab) + (b^2 + 2b^2)$
• $(3a^2 + 3a^2) + -5ab + (-8ab) + b^2 + (-2b^2)$
• $(3a^2 + 3a^2) + -5ab + (-2b^2) + b^2 + (-8ab)$

complete
complete the statement.
$(3a^2 - 5ab + b^2) - (-3a^2 + 2b^2 + 8ab) = $

• $6a^2 - 13ab - b^2$
• $6a^2 - 3ab - 3b^2$
• $-13ab - b^2$
• $-3ab - 3b^2$

Explanation:

For the question "Complete the statement. \((3a^{2}-5ab + b^{2})-(-3a^{2}+2b^{2}+8ab)=\)":

Step 1: Rewrite subtraction as addition of additive inverse

We know that \(A - B=A+(-B)\). So, \((3a^{2}-5ab + b^{2})-(-3a^{2}+2b^{2}+8ab)=(3a^{2}-5ab + b^{2})+(3a^{2}-2b^{2}-8ab)\) (since the additive inverse of \(-3a^{2}+2b^{2}+8ab\) is \(3a^{2}-2b^{2}-8ab\)).

Step 2: Group like terms

Group the terms with \(a^{2}\), \(ab\), and \(b^{2}\) respectively:
\((3a^{2}+3a^{2})+(-5ab-8ab)+(b^{2}-2b^{2})\)

Step 3: Combine like terms

• For \(a^{2}\) terms: \(3a^{2}+3a^{2} = 6a^{2}\)
• For \(ab\) terms: \(-5ab-8ab=-13ab\)
• For \(b^{2}\) terms: \(b^{2}-2b^{2}=-b^{2}\)

So, combining these results, we get \(6a^{2}-13ab - b^{2}\)

Answer:

\(6a^{2}-13ab - b^{2}\)